Flexibility of thought and action is a hallmark of human and animal behavior. While the basic mechanism of long-timescale flexibility (synaptic modifications) is largely agreed upon, the neural signatures and mechanistic underpinnings of short-timescale flexibility are not yet understood. Here we investigate the motor cortex (i.e., the primary motor cortex and adjacent premotor areas), which participates in the production of a great variety of behaviors, each requiring different internal computations. Yet it remains unknown how the motor cortex accomplishes this flexibility. Indeed, we lack two very basic pieces of knowledge. First, what physical mechanisms could allow such flexibility? Second, what are the empirical signatures of such mechanisms; how could they be recognized in neural response data? Unfortunately the currently available conceptual and analytical tools are ill-suited to study flexibility- e.g., a typical approach is to characterize a fixed relationship between a neuron's response patterns and a measured stimulus or movement parameter. Viewed using standard tools, neurons in many cognitive and motor areas appear to display complex responses that have little if any reliable relationship with identified quantities. This raises a difficult question: how should one attempt to characterize a system whose central feature is flexibility? A key first step is to be able to identify neural signatures of changing computations. Fortunately, modern theoretical neuroscience offers a key idea: large recurrent networks are reservoirs of response components from which complex computations can be built. Different computations require different components, and components are a unique weighted combination of neurons - a single 'neural dimension' within the n -dimensional space of n neurons. Thus, different computations occur in 'orthogonal subspaces' - disjoint sets of neural dimensions. Does this computational structure exist in biological neural networks? Answering this question requires experiments and analytical tools that can identify this potential signature of flexibility within a population of heterogeneous neural responses. RELEVANCE (See instructions): This project will advance understanding of the ability of the motor cortical system to flexibly and quickly change the computation it performs. This research will have biomedical impact that directly speaks to NINOS goals: improved understanding of the neural basis of movement should lead to better prosthetic technologies, assistive technologies, and treatments for the millions who suffer from motor disorders.